Why why why? Sum of torque, changes in directions? This is

[riseofphoenix]

Why oh WHY do the arrows in this TORQUE problem keep alternating between SINE and COS

This is what they did:

I understand the whole Torque = F * r, but WHY (at the top of the diagram) is the arrow pointing up = (25 N)cos 30 and NOT sin and why is the arrow pointing to the right underneath it (25 N)sin 30 and not cos?? Same goes for the other arrows...I thought the x-axis (horizontal) was ALL COSINE and the y-axis (vertical) was SINE. This is so frustrating!
They keep doing this in ALL of their problems and it really confuses me.
They keep changing it from left to right...please help!

 

[PhizKid]

Forget the axes. Form triangles with the angles and determine the trig functions for the sides of the triangles you are looking for

 

[TSny]

Review the definition of torque. If you write torque as F*r (where r is the distance from the axis to the point of application of the force), then F is the component of the force that acts perpendicular to r. Thus, the formula should be \tau = $F_{\bot}\:r$ where $F_{\bot}$ is the perpendicular component of the force.

[Edit: Ah, I think I misunderstood your difficulty. You are having trouble with finding the perpendicular component of the force. Follow PhizKid's advice! (You would use the cosine function for the x-component of a force only if the angle is measured from the x-axis.)]

 

[riseofphoenix]

Forget the axes. Form triangles with the angles and determine the trig functions for the sides of the triangles you are looking for

Ohhhh!
Ok.
Thanks!